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ERP.py
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ERP.py
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## Python module for Earth rotation data
## Lisa Neef, 22 April 2014
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from scipy.io import netcdf
import csv
import experiment_settings as es
#---also include some constants in this module
# these are all taken from Gross, 2009
M_atm = 5.1441e18 # mass of the atmosphere in kg
M_oc = 1.4e21 # mass of the ocena in kg
Q = 7.292115e-5 # rot. rate of the earth in rad/s
M = 5.9737e24 # mass of the earth in kg
C = 8.0365e37 # axial principal moment of inertia (kg m2)
B = 8.0103e37 # next-largest principal MOI (kg m2)
A = 8.0101e37 # next-largest principal MOI (kg m2)
CminusA = 2.6398e35 # kg m2
CminusB = 2.6221e35 # kg m2
BminusA = 1.763e33 # kg m2
Re_m = 6.371e6 # radius of earth (m)
Re_km = 6371.0 # radius of earth (km)
g = 9.81 # grav constant in m/s2
# crust and mantle parameters
Mm = 4.0337e24 # mass of mantle (km)
Cm = 7.1236e37 # principal MOI of mantle (kgm^2)
Am = 7.0999e37 # next-largest MOI (kgm^2)
# other conversions, etc.
rad2microas = (180/np.pi)*60*60*1e6 # radians to micro arcseconds
rad2mas = (180/np.pi)*60*60*1e3 # radians to milli arcseconds
LOD0_ms = 86160*1e3 # sidereal LOD in milliseconds.
LOD0_nominal_ms = 86400*1e3 # nominal LOD in milliseconds.
# parameters used in DART AAM observation operator (IERS conventions 2003)
k2 = 0.295 # rotational Love number degree 2
ks = 0.9383 # secular (fluid limit) Love number
kl =-0.301 # load Love number
C = 8.0365E37 # (3,3) component Earth tensor of inertia
A = 8.0101E37 # (1,1) component Earth tensor of inertia
Cm = 7.1237E37 # (3,3) component core tensor of inertia
Am = 7.0999E37 # (1,1) component core tensor of inertia
g = 9.81E0 # Earth's mean gravity acceleration [m/s^2]
omega = 7.292115E-5 # Earth's mean angular velocity [s-1]
def read_aefs_iers(hostname):
# read in the AAM excitation function data from the IERS
# file path depends on the host
FP = es.iers_file_paths(hostname,'AAM')
ff = FP
# read in the ERP data
data = np.genfromtxt(ff, dtype=float, skip_header=2)
mjd = data[:,0]
x = data[:,1]
y = data[:,3]
dlod = data[:,9]
# define some constants
sigc = 2*np.pi/433;
# rotate the polar motion terms to the proper reference frame
# where X(t) = p(t)+(i/sigma)*deriv(p(t))
xdot = np.gradient(x)
ydot = np.gradient(y)
X1 = x+ydot/sigc
X2 = -y+xdot/sigc
return mjd,X1,X2,dlod
def read_erps(hostname):
# read in the Earth Rotation Parameter data from the IERS
# file path depends on the host
ff = es.iers_file_paths(hostname,'ERP')
# read in the ERP data
data = np.genfromtxt(ff, dtype=float, skip_header=2)
mjd = data[:,0]
x = data[:,1]
y = data[:,3]
dlod = data[:,9]
# define some constants
sigc = 2*np.pi/433;
# rotate the polar motion terms to the proper reference frame
# where X(t) = p(t)+(i/sigma)*deriv(p(t))
xdot = np.gradient(x)
ydot = np.gradient(y)
X1 = x+ydot/sigc
X2 = -y+xdot/sigc
return mjd,X1,X2,dlod
def iers_file_paths(hostname,data_type):
if (data_type == 'ERP'):
# path to the IERS earth rotation data
FP = {'blizzard' : '/work/bb0519/b325004/IERS-ERP/C04_1962_2010_notides.txt'
}
if (data_type == 'AAM'):
# path to the IERS earth rotation data
FP = {'blizzard' : '/work/bb0519/b325004/IERS-ERAinterim/'
}
return FP[hostname]
def eam_weights(lat,lon,comp,variable):
# retrieve a lat/lon matrix of the weights needed to compute atmospheric excitation functions
# given input latitude and longitude arrays, a vector component of AAM, and the variable
# that we want to apply the weights to
# temp inputs
#lon = np.arange(0,361.,1.)
#lat = np.arange(-90,91.,1.)
#comp = 'X1'
#variable = 'U'
# what factor do we want to compute the weights for?
cc = comp+variable
# make radian arrays
rlon = lon*np.pi/180.;
rlat = lat*np.pi/180.;
[LAT,LON] = np.meshgrid(rlat,rlon);
# list the possible conditions we can have
condX1 = [cc == 'X1PS',cc == 'X1U',cc == 'X1V']
condX2 = [cc == 'X2PS',cc == 'X2U',cc == 'X2V']
condX3 = [cc == 'X3PS',cc == 'X3U',cc == 'X3V']
condlist = condX1+condX2+condX3
# list the possible outcomes
choiceX1 = [np.sin(LAT)*np.cos(LAT)*np.cos(LAT)*np.cos(LON),np.sin(LAT)*np.cos(LAT)*np.cos(LON),-np.cos(LAT)*np.sin(LON)]
choiceX2 = [np.sin(LAT)*np.cos(LAT)*np.cos(LAT)*np.sin(LON),np.sin(LAT)*np.cos(LAT)*np.sin(LON),np.cos(LAT)*np.cos(LON)]
choiceX3 = [np.cos(LAT)*np.cos(LAT)*np.cos(LAT),np.cos(LAT)*np.cos(LAT),LAT*0]
choicelist = choiceX1+choiceX2+choiceX3
return np.select(condlist,choicelist)
def aef_massintegral(VV,PS,p,lat,lon,variable_name,ERP='X3'):
# goven a grid of U,V, or surface pressure, plus a 3D pressure grid, integrate
# the variable field to get the corresponding AAM term.
# figure out some stuff concerning the grid
nlat,nlon,nlev = p.shape
# some abbreves
radian = np.pi/180.
rlat = radian*lat
rlon = radian*lon
coslat = np.cos(rlat)
sinlat = np.sin(rlat)
coslon = np.cos(rlon)
sinlon = np.sin(rlon)
# find the area of gridboxes, which is only a function of latitude
dlon = radian*np.abs(lon[0]-lon[1])
area_horiz = np.zeros(shape=lat.shape)
# interior latitude bands
for j in range(1,nlat-1):
dlat = lat*0
dlat = radian*abs(lat[j-1] - lat[j+1])/2.0
area_horiz[j] = dlat*dlon*(Re_m**2)*np.cos(lat[j]*radian)
# north pole latband
if (np.abs(lat[0]) + np.abs(lat[0]-lat[1])/2.0 > 90.0):
alpha = radian*(90.0-np.abs(lat[1]))
area_horiz[0] = 2.0*np.pi*(Re_m**2)*(1.-np.cos(alpha))/nlon
else:
# if the pole is the actual boundary, then it's just a square pixel
dlat=radian*abs(lat[0]-lat[1])
area_horiz[0]=dlat*dlon*(Re_m**2)*np.cos(lat[0]*radian)
# south pole latband
if (np.abs(lat[nlat-1]) + np.abs(lat[nlat-1]-lat[nlat-2])/2.0 > 90.0):
# in this case, make south pole into southern boundary, compute area of circle
alpha = radian*(90.0-np.abs(lat[nlat-2]))
area_horiz[nlat-1] = 2.0*np.pi*(Re_m**2)*(1.-np.cos(alpha))/nlon
else:
dlat=radian*abs(lat[nlat-2]-lat[nlat-1])
area_horiz[nlat-1]=dlat*dlon*(Re_m**2)*np.cos(lat[nlat-1]*radian)
# prefactors -- this is taken straight from the EAM observation operator
alp1 = 1E0 / ( 1E0 - k2/ks) # rotational deformation
alp2 = 1E0 / ( 1E0 + (4E0/3E0) * (k2/ks) * (C-A)/C ) # rotational deformation
alp3 = 1E0 + kl # loading
alp4 = (C-A) / (Cm-Am) # core decoupling
alp5 = C / Cm # core decoupling
chifacprs1 = alp1 * alp3 * alp4 / (C-A)
chifacprs2 = alp1 * alp3 * alp4 / (C-A)
chifacprs3 = alp2 * alp3 * alp5 / C
chifacwin1 = alp1 * alp4 / (C-A) / omega
chifacwin2 = alp1 * alp4 / (C-A) / omega
chifacwin3 = alp2 * alp5 / C / omega
# start with zero AAM and then add up
AAM = 0.0
if variable_name is 'PS':
nlat2,nlon2 = VV.shape
dm = np.zeros(shape=(nlat2,nlon2))
x = np.zeros(shape=(nlat2,nlon2))
# for mass term, loop over lat and lon and add up the mass for each column
for ilat in range(nlat2):
for ilon in range(nlon2):
dm[ilat,ilon] = VV[ilat,ilon] * area_horiz[ilat] / g
# mass increment for each column:
if ERP is 'X1':
x[ilat,ilon] = -(Re_m**2)*coslat[ilat]*sinlat[ilat]*coslon[ilon]*chifacprs1*dm[ilat,ilon]
if ERP is 'X2':
x[ilat,ilon] = -(Re_m**2)*coslat[ilat]*sinlat[ilat]*sinlon[ilon]*chifacprs2*dm[ilat,ilon]
if ERP is 'X3':
x[ilat,ilon] = (Re_m**2)*coslat[ilat]*coslat[ilat]*chifacprs3*dm[ilat,ilon]
AAM = AAM + x[ilat,ilon]
else:
nlat2,nlon2,nlev2 = VV.shape
# compute the pressure increments for each layer
dlev = p*0
for j in range(nlat):
for i in range(nlon):
dlev[j,i,0] = 0.5*(p[j,i,0] + p[j,i,1]) # top layer
dlev[j,i,nlev-1] = PS[j,i] - 0.5*(p[j,i,nlev-2]+p[j,i,nlev-1] ) # bottom layer
for k in range(1,nlev-1):
dlev[j,i,k] = 0.5*(p[j,i,k+1] - p[j,i,k-1] ) # inner layers
# for wind terms, loop over lat, lon, lev, and compute the AM contribution for each box
dm = dlev*0
x = np.zeros(shape=(nlat2,nlon2))
dm = np.zeros(shape=(nlat2,nlon2,nlev))
for k in range(nlev):
for ilat in range(nlat2):
for ilon in range(nlon2):
dm[ilat,ilon,k] = dlev[ilat,ilon,k] * area_horiz[ilat] / g
if (variable_name is 'US') or (variable_name is 'U'):
if ERP is 'X1':
x[ilat,ilon] = x[ilat,ilon] - Re_m*VV[ilat,ilon,k]*sinlat[ilat]*coslon[ilon]*dm[ilat,ilon,k]
if ERP is 'X2':
x[ilat,ilon] = x[ilat,ilon] - Re_m*VV[ilat,ilon,k]*sinlat[ilat]*sinlon[ilon]*dm[ilat,ilon,k]
if ERP is 'X3':
x[ilat,ilon] = x[ilat,ilon] + Re_m*VV[ilat,ilon,k]*coslat[ilat]*dm[ilat,ilon,k]
if (variable_name is 'VS') or (variable_name is 'V'):
if ERP is 'X1':
x[ilat,ilon] = x[ilat,ilon] + Re_m*VV[ilat,ilon,k]*sinlon[ilon]*dm[ilat,ilon,k]
if ERP is 'X2':
x[ilat,ilon] = x[ilat,ilon] - Re_m*VV[ilat,ilon,k]*coslon[ilon]*dm[ilat,ilon,k]
if ERP is 'X3':
x[ilat,ilon] = 0.0
#aamu = + Re_m*VV[45,90,k]*coslat[45]*dm[45,90,k]
# now loop over lat and lon and add up AAM:
for ilat in range(nlat2):
for ilon in range(nlon2):
if ERP is 'X1':
AAM = AAM + x[ilat,ilon]*chifacwin1
if ERP is 'X2':
AAM = AAM + x[ilat,ilon]*chifacwin2
if ERP is 'X3':
AAM = AAM + x[ilat,ilon]*chifacwin3
return AAM
def aef(field,lev,lat,lon,variable_name,ERP='X3'):
# given some variable field (U, V, or surface pressure), compute the AAM excitation function for the desired Earth rotation parameters
# check whether pressure levels are in Pascale (not hPa) -- send an alert if this is not the case
if np.max(lev) < 8E4:
print('the pressure at the surface is '+str(np.max(lev))+' which means these levels are probably not in Pascal')
print('returning...')
return None
# reshape the variable array to be lev x lat x lon, or lat x lon
ndim = len(field.shape)
nlat = len(lat)
nlon = len(lon)
if ndim == 2:
V = np.reshape(field,(nlat,nlon))
if ndim == 3:
nlev = len(lev)
V = np.reshape(field,(nlat,nlon,nlev))
# load the appropriate geographic weighting function for the desired variable and ERP, and
# multiply the field by this
W0 = eam_weights(lat,lon,ERP,variable_name)
#W = np.reshape(W0,(nlat,nlon))
W = np.transpose(W0)
if ndim == 2:
Vw = V*W
else:
Vw = V*0
for ilev in range(nlev):
Vw[:,:,ilev] = V[:,:,ilev]*W
# convert lat and lon to radians
rlon=lon*np.pi/180
rlat=lat*np.pi/180
# the integrals have to be multiplied by -1 if the lat, lon, or lev arrays are defined in the other direction
# the "right" direction is lat -90-90, lon 0-360, and ps to ptop
latfac = 1.0
lonfac = 1.0
levfac = 1.0
if lat[0] > lat[nlat-1]:
latfac = -1.
if lon[0] > lon[nlon-1]:
lonfac = -1.
if not (variable_name == 'PS'):
if lev[0] < lev[nlev-1]:
levfac = -1.
# I have no idea why this needs to be positive for CAM, but that seems to be the only way to rectivy the diff between the vol and mass integral
levfac = 1.0
if variable_name == 'PS':
# surface pressure: integrate over lat and lon
Vlon = lonfac*np.trapz(Vw,rlon)
Vint = latfac*np.trapz(Vlon,rlat)
else:
# meridional and zonal wind: integrate over lat,lon,lev
# integral over lon:
Vlon = np.zeros(shape=(nlat,nlev))
for k in range(nlev):
Vlon[:,k] = lonfac*np.trapz(Vw[:,:,k],rlon)
# integral over lev:
Vlevlon = levfac*np.trapz(Vlon,lev)
# integral over lat:
Vint = latfac*np.trapz(Vlevlon,rlat)
# multiply by the prefactors that give us AAM:
fac = aam_prefactors(ERP,variable_name)
AAM = fac*Vint
return AAM
def aam_prefactors(comp,variable_name):
# return the geophysical prefactors needed to compute the angular momentum components.
# this is taken straight from the EAM observation operator
#alp1 = 1E0 / ( 1E0 - k2/ks) # rotational deformation
#alp2 = 1E0 / ( 1E0 + (4E0/3E0) * (k2/ks) * (C-A)/C ) # rotational deformation
#alp3 = 1E0 + kl # loading
#alp4 = (C-A) / (Cm-Am) # core decoupling
#alp5 = C / Cm # core decoupling
#chifacprs1 = alp1 * alp3 * alp4 / (C-A)
#chifacprs2 = alp1 * alp3 * alp4 / (C-A)
#chifacprs3 = alp2 * alp3 * alp5 / C
#chifacwin1 = alp1 * alp4 / (C-A) / omega
#chifacwin2 = alp1 * alp4 / (C-A) / omega
#chifacwin3 = alp2 * alp5 / C / omega
if (comp=='X1') or (comp=='X2'):
if (variable_name == 'U') or (variable_name == 'V'):
fac = (-1.591*Re_m**3)/(Q*g*CminusA)
ff = 1/(1-k2/ks)
fac2 = (-ff*Re_m**3)/(Q*g*CminusA)
if (variable_name == 'PS'):
fac = (-1.098*(Re_m**4))/(g*CminusA)
ff = (1+kl)/(1-k2/ks)
fac2 = (-ff*(Re_m**4))/(g*CminusA)
if (comp=='X3'):
if (variable_name == 'U') or (variable_name == 'V'):
fac = (0.997*(Re_m**3))/(Q*g*Cm);
top = 1.0
bot = (1.+(4./3.)*(k2/ks)*(C-A)/C)
ff = top/bot
fac2 = (ff*(Re_m**3))/(Q*g*Cm)
if (variable_name == 'PS'):
fac = (0.748*(Re_m**4))/(g*Cm)
top = (1.+kl)
bot = (1.+(4./3.)*(k2/ks)*(C-A)/C)
ff = top/bot
fac2 = (ff*(Re_m**4))/(g*Cm)
return fac2